Various types of carton clamps have been proposed for use with lift trucks in order to provide damage-free clamping, particularly with unitized case loads. The proposals have included arm camber, and toe-in and articulating arm designs. The present invention is directed to a carton clamp having clamp arms which apply an equal pressure over the entire pad surface meaning that every tier of the load supports its own weight and allows the pads to grip cartons firmly, but gently. The equal pressure design of the present invention not only implements a vertical, but also the more importantly horizontal (front to back) distribution of pressure on the load/cases.